Dynamics of a chain system of rigid bodies with gravity-friction seismic dampers: fixed supports


A design model for a chain system of N elastically linked rigid bodies with a spheroidal gravity-friction damper is proposed. The Lagrange–Painlevé equations of the first kind are used to construct nonlinear dynamical models of a mechanical system undergoing translational vibrations about the equilibrium position. The conditions under which the system moves in one plane are established. The double nonstationary phase–frequency resonance of a system with N = 2 is analyze. After the numerical integration of the systems of differential equations, the phase–frequency surfaces are plotted and examined for several combinations of system parameters under two-frequency loading


chain system rigid body seismic damper forced vibrations double phase–frequency resonance two-frequency loading phase–frequency surfaces 


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Copyright information

© Springer Science+Business Media, Inc. 2009

Authors and Affiliations

  1. 1.S. P. Timoshenko Institute of MechanicsNational Academy of Sciences of UkraineKyivUkraine

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